research article design method for channel diffusers of centrifugal...

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2013 Article ID 589357 7 pageshttpdxdoiorg1011552013589357

Research ArticleDesign Method for Channel Diffusers ofCentrifugal Compressors

Mykola Kalinkevych and Andriy Skoryk

Technical Thermophysics Department Sumy State University 2 Rimsky-Korsakov Street Sumy 40007 Ukraine

Correspondence should be addressed to Andriy Skoryk avsrsmailru

Received 29 April 2013 Revised 14 July 2013 Accepted 20 July 2013

Academic Editor Enrico Sciubba

Copyright copy 2013 M Kalinkevych and A Skoryk This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The design method for channel diffusers of centrifugal compressors which is based on the solving of the inverse problem of gasdynamics is presented in the paper The concept of the design is to provide high pressure recovery of the diffuser by assuming thepreseparation condition of the boundary layer along one of the channel surfacesThe channel diffuser was designed with the use ofdevelopedmethod to replace the vaned diffuser of the centrifugal compressormodel stageThenumerical simulation of the diffuserswas implemented by means of CFD software Obtained gas dynamic characteristics of the designed diffuser were compared to thebase vaned diffuser of the compressor stage

1 Introduction

The operating conditions and purpose of centrifugal com-pressor should be taken into account when choosing thetype of its diffuser Channel diffusers (CD) could be morepreferable as compared to other types in the following cases(1) at small flow angles at the diffuser inlet (2) when the gaspasses from the diffuser channels to the separated cameras(3) if the diffuser channels turn to the channels of the returnelement of compressor

Traditional geometry of channel diffusers includes theinitial section shaped as a logarithmic spiral along one ofthe vane surfaces and the main section with straight walls(Figure 1(a))The channel diffusers with wedge vanes are alsowidely used (Figure 1(b))

Some authors recommend using the Reneau et al [1] andRunstadler Jr and Dean Jr [2] database for the flat planediffusers to design wedge-shaped channel diffusers Kano etal [3] and Clements and Artt [4] indicated that such datacannot be used to design the high-performance diffuser ofcentrifugal compressor because of the distorted three-dimen-sional swirled flow at the inlet In addition such a databasedoes not cover the wide range of geometries and inlet flowconditions

Generally the most effective vane geometry may beobtained by solving the inverse problem of gas dynamicsThe maximum pressure rise in diffuser may be achievedwhen the flow is close to separation Stratford [5] obtainedexperimentally the flow with stable preseparation conditionof the boundary layer along one of the surfaces of the two-dimensional diffuser It was shown that by specifying thepreseparation pressure distribution the required pressurerisemay be attained in the shortest possible distance andwiththe least possible dissipation of energy for a given diffuserdimensions and initial boundary layer Such approach waslater used by Liebeck [6] for estimation of the shape of highlift airfoil and by Hobbs and Weingold [7] for designingthe high performance axial compressor airfoils Howeverthere is no information in applying the preseparation velocity(or pressure) distributions for the design of centrifugalcompressor cascades with radial swirled flow

Kalinkevych et al [8] showed that efficiency of the vaneddiffuser (VD) of centrifugal compressor may be improved byusing such a concept In this work the center line shape of thevanes with constant thickness was obtained by defining thepreseparation velocity distribution along the pressure surfaceof the vane

2 International Journal of Rotating Machinery

(a) (b)

Figure 1 Channel diffusers of traditional geometry (a) channel diffuser with initial section shaped as a logarithmic spiral (b) channel diffuserwith wedge vanes

The principles of design method for high-performancechannel diffusers (CD) of centrifugal compressors in whichvane thickness increases along the radius are presented in thepaper

2 Design Method

According to the presented method the diffuser design isbased on assuming the preseparation condition of the bound-ary layer along one of the vane surfaces Mathematical modelfor solving the inverse problem of gas dynamics is developedfor the steady adiabatic gas flow without separations

The angular momentum change about axis 119911 for theannular element of gas with width Δ119887 and mass flow rate Δ119898from the diffuser inlet 119903in to the current section 119903 (Figure 2)is as follows

Δ119872 = Δ119898 sdot (119903in sdot 119888in sdot cos120572in minus 119903 sdot 119888 sdot cos120572) (1)

Moment of forces acting on the 119911V vanes of diffuser from 119903into 119903 is as follows

Δ119872 = Δ119887 sdot 119911V sdot int

119903

119903in

Δ119901 sdot 119903 sdot 119889119903 (2)

Continuity equation is of the form

Δ119898 = 119888119903sdot 120588 sdot 2120587 sdot 119903 sdot Δ119887 sdot 120591 (3)

Equations (1) (2) and (3) may be represented using gasdynamics relations for isentropic flow

119903in sdot 120582in sdot cos120572in minus 119903 sdot 120582 sdot cos120572

=

119887 sdot 119911V sdot 119901lowast

in119898 sdot 119886cr

sdot int

119903

119903in

[120587 (120582ps) minus 120587 (120582ss)] sdot 119903 sdot 119889119903

119898 = 120582 sdot 120576 (120582) sdot 119886cr sdot 120588lowast

sdot 2120587 sdot 119903 sdot 119887 sdot 120591 sdot sin120572

(4)

rrin

Δb

b

120572c

Figure 2 Channel diffuser scheme

where 120582 120582ps and 120582ss (119886cr = radic(2120574(120574 + 1))119877119879lowast is the critical

velocity) are the mean flow velocity within the diffuser chan-nel velocity along the pressure surface and velocity along thesuction surface of the vane respectively and 120572 is the meanflow angle within the diffuser channel

Pressure and density relations are determined as a func-tion of velocity

120587 (120582) =

119901

119901lowast= (1 minus

120574 minus 1

120574 + 1

sdot 1205822

)

120574(120574minus1)

120576 (120582) =

120588


120574 minus 1

120574 + 1

sdot 1205822

)

1(120574minus1)

(5)

The blockage factor is given by the following equation

120591 = 1 minus

1205751015840

sdot 119911V

2120587 sdot 119903 sdot sin120572 (6)

where 1205751015840

= 120575V + sum120575lowast is the modified vane thickness 120575V

is vane thickness and sum120575lowast is total displacement thickness

of boundary layers in the vane channel estimated using theLoitcyanskii method [9]

International Journal of Rotating Machinery 3

Velocity distribution which provides the preseparationcondition of the boundary layer along the pressure surfaceof the vane is defined by the formula [8]

120582ps = 1205821sdot [1 +

(119897 minus 1198971) sdot (2 + 119867

119904) sdot (minus119891

119904)

120575

lowastlowast

1

]

minus1(2+119867119904)

(7)

Parameters marked with subscript ldquo1rdquo are the coefficientswhich affect the given velocity distribution quantitatively

The set of (4) includes unknowns 120582 120575V and 120582ss Thedependence 120572 = 119891(119903)may be given as linear

For linear pressure distribution along the vane pitch therelation between the velocities may be defined as

120587 (120582ps) + 120587 (120582ss) = 2 sdot 120587 (120582) (8)

By substituting equation (8) into equation (4) equation(4) can be solved using numerical methods for numericalintegration and root finding

The initial data for the design are(i) gas properties (119877 120574 ])(ii) static pressure 119901in and static temperature 119879in at dif-

fuser inlet(iii) inlet and outlet flow angles (120572in 120572out)(iv) mass flow rate(v) geometrics of the meridional contour(vi) quantity of vanes 119911V(vii) mean flow angle distribution along the diffuser chan-

nel (120572 = 119891(119903))As a result of calculation the vane thickness distributionalong the radius 120575V = 119891(119903) is estimated so the geometry ofthe vane is totally defined

The compressor design point flow parameters at theimpeller exit are used as mentioned in above initial data forthe diffuser design Presented design method is valid for thesubsonic flow along the entire diffuser

3 Application of the Design Method forthe Centrifugal Compressor Model Stage

Using presented method the CD for the model centrifugalcompressor stage of JSC ldquoSumy Frunze NPOrdquo was designedThe design was implemented for the parameters at thediffuser inlet at the design point of the stage The parametersof the flowwere obtained by numerical simulation of the basemodel compressor stage with VD

The values of design parameters are shown in Table 1Themeridional contour geometry inlet and outlet angles of thevanes are the same as for the base VD

Thegiven velocity distribution for theCDdesign is shownin Figure 3 The geometry parameters of the vane are shownin Figure 4 Vane thickness distribution was obtained as aresult of design calculation

The relative radius in Figures 3 and 4 is defined by formula

119903119894=

119903119894minus 119903in

119903out minus 119903in (9)

Table 1 Initial data for channel diffuser design

Design parameter ValuePressure at the diffuser inlet Pa 118000Temperature at the diffuser inlet K 319Mass flow rate kgs 1775Quantity of vanes 17Inlet radius 119903

3 m 02622

Outlet radius 1199034 m 03092

Width of diffuser 1198873 m 00155

Vane leading edge thickness m 0003Vane leading edge centerline angle 120572

3V∘ 22

Vane trailing edge centerline angle 1205724V∘ 37

0

01

02

03

04

05

06

0 02 04 06 08 1

120582 120582

120582ss

120582ps

ri

Figure 3Given velocity distribution for the channel diffuser design

The comparison between the vane channels of the base VDand designed CD is shown in Figure 5

4 Numerical Simulation

Numerical simulation was performed by use of commercialCFD software ANSYS CFX v14 for two different compressorstages The first one is the model compressor stage of JSCldquoSumy Frunze NPOrdquo with base VDThe second stage has thesame impeller as the first The only difference is the diffuserwhich was designed using presented method (see Section 3)

41 Grid Quality and Preprocessor Setup The steady-statemodel and high resolution discretization scheme were usedfor simulations SST-turbulence model is the most acceptablemodel for the centrifugal compressor flow simulations [10]which in the case of sufficient grid refinement shows appro-priate results for the near-wall boundary layers and flow core

The structured hexahedral grids for impeller and diffuserswere created in ANSYS TurboGrid While creating the near-wall prismatic layers it was checked that value of 119910+ is lessthan 2The quantity of grid points within the boundary layerswas no less than 20 The coarser grid was created for the flowcore which is acceptable for the SST-turbulence model The


0

1

2

3

4

5

6

7

8

0 02 04 06 08 1

120575 (m

m)

ri

0

5

10

15

20

25

30

35

40

0 02 04 06 08 1

120572(∘)

ri

Figure 4 Vane thickness and angle distribution for the designed channel diffuser

Figure 5 The comparison between the base VD vane channel(black) and designed CD vane channel (red)

impeller grid consists of 690 690 elements (Figure 6(a)) TheCD grid consists of 637 296 elements (Figure 6(b)) and VDgrid (Figure 6(c)) consists of 618 618 elements Due to thedifferences in geometry of these diffusers it is not possibleto create totally topologically identical grids The parameterswhich define the topology of the near-wall prismatic layersand the quantity of grid elements in meridional plane wereidentical Therefore this topological difference is acceptablefor the comparison The difference is only in the flow coreelements quantity

Themain parameters specified inANSYSCFX preproces-sor are shown in Table 2 To connect the respective surfacesof the impeller and diffuser the interface ldquostagerdquo was usedThis type of interface is usually used for the steady state cal-culations the parameters at the interface surfaces are aver-aged circumferentially Therefore interface ldquostagerdquo is orientedfor estimating of the integral characteristics of the compressorstage

As the convergence criteria the discrepancy in static pres-sure recovery coefficient equal to 001 and in total pressureloss coefficient equal to 0005 has been used

The grid independence study showed that for the designpoint the diffusersrsquo nondimensional characteristics change isdistinct for the diffusers node quantity less than 400 000 Foroff-design conditions the results of simulation are more grid-sensitive

The main purpose of simulations was to establish themore effective diffuser by comparing their nondimensional

Table 2 Boundary conditions andmodels specified inANSYSCFXpreprocessor

Boundary or model OptionImpeller inlet Total pressure total temperatureDiffuser outlet Mass flow rateInterface type betweenimpeller and diffuser Stage

Turbulence model SSTHeat transfer model Total energyFluid model Air ideal gasWall heat transfer model Adiabatic

characteristics Generated grids were indicated as sufficientfor such calculations

To evaluate the diffuser aerodynamic performance thepressure recovery coefficient

119862119901=

119901out minus 119901in119901lowast

in minus 119901in(10)

and total pressure loss coefficient

120577 =

119901lowast

in minus 119901lowast

out119901lowast


were used

42 Simulation Results Obtained nondimensional diffusersrsquocharacteristics are shown in Figure 7 as a function of inci-dence angle

1198943= 1205723V minus 120572

3 (12)

where 1205723V is vane centerline angle at the diffuser inlet

It can be seen that characteristics of CD are better thanof VD at the range of positive incidence angles Moreovermaximal value of pressure recovery of CD is slightly higherthan of VD The shape of characteristics of CD is more flat


(a) Impeller

(b) Channel diffuser

(c) Vaned diffuser

Figure 6 Grids of the stage elements

especially for the total pressure loss coefficient In order tounderstand these results the flow pattern within the diffuserswas examined

Figure 8 presents the velocity vectors within both dif-fusers for 119894

3asymp 4∘ Predicted high loss level and low pressure

recovery of VD occur due to the wide flow separation regionDue to the high pressure gradients the flow separation occurson the suction surface of the vane and covers the area from thehub side to midspan Reducing the effective area resulted inlow pressure recovery

The flow pattern within the CD is more favorable dueto the controlled flow deceleration provided by the designedvane geometry For the operating conditions range of 119894

3asymp

0∘ndash4∘ the total losses include only the friction loss and wakemixing loss at diffuser outlet (Figures 8 and 9) Therefore theshape of the loss characteristic of CD is almost straight

As it can be seen from Figure 7 for the top pressurerecovery operating condition of VD at 119894

3asymp 1∘ the pressure

recovery of CD is slightly lower whereas the losses arepractically the same The flow separation within the CD wasdetected at 119894

3asymp 5∘

0

01

02

03

04

05

06

07

minus2 minus1 0 1 2 3 4 5

VD (CFD)

120577

CD (CFD)

Mass flow rate rise direction

Cp

i3 (∘)

Figure 7 Nondimensional characteristics of designed CD and baseVD

2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(a) Hub side

2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(b) Midspan

Figure 8 Velocity vectors for different flow surfaces of VD (top) andCD (bottom) at 119894

3asymp 4∘


211187164140117947047230

2292031781531271027651250

Velo

city

(m sminus1)

Velo

city

(m sminus1)

Figure 9 Velocity vectors for the midspan plane of VD (top) andCD (bottom) at 119894

3asymp 1∘

5 Conclusions

The numerical simulation showed the potential availabilityof the developed channel diffuser design method for thehigh-performance centrifugal compressor design Efficiencyof the compressor stage may be improved at the range of lowmass flow rates because of the flow separation prevention andfriction area decrease in the channel diffuser

The channel diffusersrsquo characteristics are more flat andstable for the positive incidence angles as compared to thevaned diffuser

At the further stage of the research the designed channeldiffuser will be tested in detail to verify the real advantages ofsuch diffuser and validation of proposed design method

Nomenclature

119903 Radius119888 Velocity120572 Mean flow angle119901 PressureΔ119901 = (119901ps minus 119901ss) Pressure difference between surfaces of

the vane120588 Density119879 Temperature120591 Blockage factor120582 = 119888119886cr Coefficient of velocity119886cr Critical sonic speed119887 Width of diffuser119898 Mass flow rate119872 Angular momentum119911V Quantity of vanes120574 Ratio of specific heats120587(120582) Gas dynamic function of pressure120576(120582) Gas dynamic function of density120575V Vane thickness

1205751015840 Modified vane thickness120575lowast Displacement thickness of boundary layer120575lowastlowast Momentum thickness of boundary layersum120575lowast Total displacement thickness of boundary

layers119897 Vane centerline length coordinate119871 Vane centerline length119897 = 119897119871 Relative length120575

lowastlowast

= 120575lowastlowast

119871 Relative momentum thickness119867119904 Boundary layer shape parameter

119891119904 Boundary layer shape parameter

] Kinematic viscosity119877 Gas constant119863 Diameter120577 Total pressure loss coefficient119862119901 Pressure recovery coefficient

Subscripts

in 3 Diffuser inletout 4 Diffuser outletps Pressure surface of the vaness Suction surface of the vane119903 Radial directioncr CriticalV Vane1 Initial condition of the boundary layerlowast Stagnation parameter119904 Preseparation condition

References

[1] L R Reneau J P Johnston and S J Kline ldquoPerformance anddesign of straight two-dimensional diffusersrdquo Journal of BasicEngineering vol 89 no 1 pp 141ndash150 1967

[2] PW Runstadler Jr and R C Dean Jr ldquoStraight channel diffuserperformance at high inlet mach numbersrdquo Journal of BasicEngineering vol 91 no 3 pp 397ndash412 1969

[3] F Kano N Tazawa and Y Fukao ldquoAerodynamic performanceof large centrifugal compressorsrdquo Journal of Engineering forPower-Transactions of the ASME vol 104 no 4 pp 796ndash8041982

[4] W W Clements and D W Artt ldquoThe influence of diffuserchannel length-width ratio on the efficiency of a centrifugalcompressorrdquo Journal of Power and Energy vol 202 no 1988 pp163ndash169 1988

[5] B S Stratford ldquoAn experimental flow with zero skin frictionthroughout its region of pressure riserdquo Journal of FluidMechan-ics vol 5 no 1 pp 17ndash35 1959

[6] R H Liebeck ldquoA class of airfoils designed for high lift inincompressible flowrdquo Journal of Aircraft vol 10 no 10 pp 610ndash617 1973

[7] D E Hobbs and H D Weingold ldquoDevelopment of controlleddiffusion airfoils formultistage compressor applicationrdquo Journalof Engineering for Gas Turbines and Power vol 106 no 2 pp271ndash278 1984

[8] M Kalinkevych O Obukhov A Smirnov and A SkorykldquoThe design of vaned diffusers of centrifugal compressors basedon the given velocity distributionrdquo in Proceedings of the 7th


International Conference on Compressors and their Systems pp61ndash69 Woodhead Publishing 2011

[9] L G LoitcyanskiiMekhanIka ZhIdkostI I Gaza [FluId Mechan-Ics (In RussIan)] Drofa Moscow Russia 2003

[10] F Menter M Kunitz and R Langtry ldquoTen years of industrialexperience with the SST turbulence modelrdquo Journal of Turbu-lence Heat and Mass Transfer vol 4 pp 625ndash632 2003

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Propagation




Navigation and Observation



DistributedSensor Networks



(a) (b)

Figure 1 Channel diffusers of traditional geometry (a) channel diffuser with initial section shaped as a logarithmic spiral (b) channel diffuserwith wedge vanes

The principles of design method for high-performancechannel diffusers (CD) of centrifugal compressors in whichvane thickness increases along the radius are presented in thepaper

2 Design Method

According to the presented method the diffuser design isbased on assuming the preseparation condition of the bound-ary layer along one of the vane surfaces Mathematical modelfor solving the inverse problem of gas dynamics is developedfor the steady adiabatic gas flow without separations

The angular momentum change about axis 119911 for theannular element of gas with width Δ119887 and mass flow rate Δ119898from the diffuser inlet 119903in to the current section 119903 (Figure 2)is as follows

Δ119872 = Δ119898 sdot (119903in sdot 119888in sdot cos120572in minus 119903 sdot 119888 sdot cos120572) (1)

Moment of forces acting on the 119911V vanes of diffuser from 119903into 119903 is as follows

Δ119872 = Δ119887 sdot 119911V sdot int

119903

119903in

Δ119901 sdot 119903 sdot 119889119903 (2)

Continuity equation is of the form

Δ119898 = 119888119903sdot 120588 sdot 2120587 sdot 119903 sdot Δ119887 sdot 120591 (3)

Equations (1) (2) and (3) may be represented using gasdynamics relations for isentropic flow

119903in sdot 120582in sdot cos120572in minus 119903 sdot 120582 sdot cos120572

=

119887 sdot 119911V sdot 119901lowast

in119898 sdot 119886cr

sdot int

119903

119903in

[120587 (120582ps) minus 120587 (120582ss)] sdot 119903 sdot 119889119903

119898 = 120582 sdot 120576 (120582) sdot 119886cr sdot 120588lowast

sdot 2120587 sdot 119903 sdot 119887 sdot 120591 sdot sin120572

(4)

rrin

Δb

b

120572c

Figure 2 Channel diffuser scheme

where 120582 120582ps and 120582ss (119886cr = radic(2120574(120574 + 1))119877119879lowast is the critical

velocity) are the mean flow velocity within the diffuser chan-nel velocity along the pressure surface and velocity along thesuction surface of the vane respectively and 120572 is the meanflow angle within the diffuser channel

Pressure and density relations are determined as a func-tion of velocity

120587 (120582) =

119901


120574 minus 1

120574 + 1

sdot 1205822

)

120574(120574minus1)

120576 (120582) =

120588


120574 minus 1

120574 + 1

sdot 1205822

)

1(120574minus1)

(5)

The blockage factor is given by the following equation

120591 = 1 minus

1205751015840

sdot 119911V

2120587 sdot 119903 sdot sin120572 (6)

where 1205751015840

= 120575V + sum120575lowast is the modified vane thickness 120575V

is vane thickness and sum120575lowast is total displacement thickness

of boundary layers in the vane channel estimated using theLoitcyanskii method [9]



120582ps = 1205821sdot [1 +

(119897 minus 1198971) sdot (2 + 119867

119904) sdot (minus119891

119904)

120575

lowastlowast

1

]

minus1(2+119867119904)

(7)




120587 (120582ps) + 120587 (120582ss) = 2 sdot 120587 (120582) (8)











119903119894=

119903119894minus 119903in

119903out minus 119903in (9)



3 m 02622




3V∘ 22


0

01

02

03

04

05

06

0 02 04 06 08 1

120582 120582

120582ss

120582ps

ri








0

1

2

3

4

5

6

7

8

0 02 04 06 08 1

120575 (m

m)

ri

0

5

10

15

20

25

30

35

40

0 02 04 06 08 1

120572(∘)

ri













119862119901=




120577 =

119901lowast


out119901lowast


were used


1198943= 1205723V minus 120572

3 (12)




(a) Impeller


(c) Vaned diffuser







3asymp





3asymp 5∘

0

01

02

03

04

05

06

07


VD (CFD)

120577

CD (CFD)


Cp

i3 (∘)


2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(a) Hub side

2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(b) Midspan


3asymp 4∘


211187164140117947047230

2292031781531271027651250

Velo

city

(m sminus1)

Velo

city

(m sminus1)


3asymp 1∘

5 Conclusions




Nomenclature





lowastlowast





Subscripts


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120582ps = 1205821sdot [1 +

(119897 minus 1198971) sdot (2 + 119867

119904) sdot (minus119891

119904)

120575

lowastlowast

1

]

minus1(2+119867119904)

(7)




120587 (120582ps) + 120587 (120582ss) = 2 sdot 120587 (120582) (8)











119903119894=

119903119894minus 119903in

119903out minus 119903in (9)



3 m 02622




3V∘ 22


0

01

02

03

04

05

06

0 02 04 06 08 1

120582 120582

120582ss

120582ps

ri








0

1

2

3

4

5

6

7

8

0 02 04 06 08 1

120575 (m

m)

ri

0

5

10

15

20

25

30

35

40

0 02 04 06 08 1

120572(∘)

ri













119862119901=




120577 =

119901lowast


out119901lowast


were used


1198943= 1205723V minus 120572

3 (12)




(a) Impeller


(c) Vaned diffuser







3asymp





3asymp 5∘

0

01

02

03

04

05

06

07


VD (CFD)

120577

CD (CFD)


Cp

i3 (∘)


2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(a) Hub side

2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(b) Midspan


3asymp 4∘


211187164140117947047230

2292031781531271027651250

Velo

city

(m sminus1)

Velo

city

(m sminus1)


3asymp 1∘

5 Conclusions




Nomenclature





lowastlowast





Subscripts


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

1

2

3

4

5

6

7

8

0 02 04 06 08 1

120575 (m

m)

ri

0

5

10

15

20

25

30

35

40

0 02 04 06 08 1

120572(∘)

ri













119862119901=




120577 =

119901lowast


out119901lowast


were used


1198943= 1205723V minus 120572

3 (12)




(a) Impeller


(c) Vaned diffuser







3asymp





3asymp 5∘

0

01

02

03

04

05

06

07


VD (CFD)

120577

CD (CFD)


Cp

i3 (∘)


2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(a) Hub side

2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(b) Midspan


3asymp 4∘


211187164140117947047230

2292031781531271027651250

Velo

city

(m sminus1)

Velo

city

(m sminus1)


3asymp 1∘

5 Conclusions




Nomenclature





lowastlowast





Subscripts


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) Impeller


(c) Vaned diffuser







3asymp





3asymp 5∘

0

01

02

03

04

05

06

07


VD (CFD)

120577

CD (CFD)


Cp

i3 (∘)


2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(a) Hub side

2332071811551291047852260

2652362061771471188859290

Velo

city

(m sminus1)

Velo

city

(m sminus1)

(b) Midspan


3asymp 4∘


211187164140117947047230

2292031781531271027651250

Velo

city

(m sminus1)

Velo

city

(m sminus1)


3asymp 1∘

5 Conclusions




Nomenclature





lowastlowast





Subscripts


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










211187164140117947047230

2292031781531271027651250

Velo

city

(m sminus1)

Velo

city

(m sminus1)


3asymp 1∘

5 Conclusions




Nomenclature





lowastlowast





Subscripts


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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